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116 and the other perpendicular, into a plane at right angles to the meridian where both components would be at right angles to the drift, and therefore where no differential effect would be produced, no change in the field of view could be detected. Had there been a total difference of 7.8 x 10-13 of the whole velocity between the components, the effect would have been manifest. We may, therefore, conclude that there is no third order effect. How well the various theories of a quiescent ether will lend themselves to this further adaptation remains to be seen, but undoubtedly by properly choosing the coefficients it may be done; however, any theory which does not contain explicitly the exact and complete adaptation to all orders of the aberration must certainly impress itself as highly artificial in its successive auxiliary hypotheses and approximations.

Larmor, in reference to his theory, says, "It is, in fact, found that the Maxwellian circuital equations of sethereal activity, in the ambient aether referred to axes moving along with the uniform velocity of convection, v, can be reduced to the same form as for axes at rest up to and including $$\left(\tfrac{v}{V}\right)^{2}$$ but not $$\left(\tfrac{v}{V}\right)^{3}$$ by adopting certain coefficients." "If, then, matter is for physical purposes a purely ethereal system, if it is constituted of simple polar singularities or electrons, positive and negative, in the Maxwellian aether, the nuclei of which may be either practically points or else small regions of aether with internal connections of pure constraint, the propositions above stated v for the first order are extended to the second order of $$\tfrac{v}{V}$$ with the single addition of the Fitzgerald-Lorentz shrinkage in the scale of space and an equal one in the scale of time, which, being isotropic, is unrecognizable." "On such a theory as this the criticism presents itself, and was in fact at once made, that one hypothesis is needed to annul optical effects to the first order; that when these were found to be actually null to the second order, another hypothesis had to be added: and that another hypothesis would be required for the third order, while in fact there was no reason to believe that they were not exactly null to all orders. Such a train of remarks indicates that the nature of the hypothesis has been overlooked. And if indeed it could be proved that the optical effect is null up to the third order, that circumstance would not demolish the theory, but would rather point to some finer adjustment than it provides for; needless to say the attempt would indefinitely transcend existing experimental possibilities." And further, "up to the first order the electron hypothesis, that electricity is atomic, suffices by itself, as Lorentz was first to show." "Up to the second order, the hypothesis that matter is constituted electrically—of electrons—is required in addition."

The necessity in view of the present experimental data for leaving